Functions 3 Question 1

1. If X and Y are two non-empty sets where f:XY, is function is defined such that

f(C)=f(x):xC for CX and f1(D)=x:f(x)D for DY

for any AY and BY, then

(2005, 1M)

(a) f1f(A)=A

(b) f1f(A)=A, only if f(X)=Y

(c) ff1(B)=B, only if Bf(x)

(d) ff1(B)=B

Show Answer

Answer:

Correct Answer: 1. (c)

Solution:

  1. Given, function f:R1,1A defined as

f(x)=x21x2=yx2=y(1x2)x2(1+y)=yx2=y1+y [provided y1]x20y1+y0y(,1)[0,)

Since, for surjective function, range of f= codomain

Set A should be R[1,0).



जेईई के लिए मॉक टेस्ट

एनसीईआरटी अध्याय वीडियो समाधान

दोहरा फलक